How to get the active strips in the NLA editor from Python?
You can get the active NLA track, but the strips array has no property .active in the Python API. It's not exposed, but the active strip is known in the C code (note that the 
Active Strip panel is hardcoded).

All you can do with Python is to get all selected strips:

try:
    selected_strips = [strip for strip in bpy.context.object.animation_data.nla_tracks.active.strips if strip.select]
except AttributeError:
    selected_strips = []